Logan Couture and Brent Burns scored for the Sharks, who lost their fifth straight at home and four of five overall.

Ben Bishop stopped 33 of 35 shots as Tampa Bay won in San Jose for the first time in 12 years. Antti Niemi made 28 saves.

Stamkos scored with 16 seconds left in the first period on a slap shot from just inside the blue line.

Killorn scored at 7:12 of the second period, redirecting Callahan’s shot. Stamkos picked up a rebound to set up the score.

Couture made it 2-1 with a nice shot into the upper left corner after taking a pass from Matt Nieto at 10:27 of the second.

Palat scored an unassisted goal 10 seconds into the third period.

Burns brought the Sharks within 3-2 with a backhand chip shot on a power play at 11:38 of the third period.

Paquette’s goal gave the Lightning a two-goal lead and Callahan scored an empty-net goal.

NOTES: Paquette returned to the lineup after missing two games with an upper body injury. … Sharks C Joe Thornton recorded his 891st assist, tied for 20th on the career list. … The Sharks sent D Dylan DeMelo to AHL Worchester to make room for D Marc-Edouard Vlasic, who came off the injured reserve list after missing four games.